Answer:
Slope: -3/4
y-intercept: (0,-5)
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
So line QP is the tangent which means angle Q is 90 degrees. All three angles of a triangle added together is 180 degrees so:
x = 180 - 90 - 12
x = 78
Answers:
- (a) 1/10
- (b) 3/10
- (c) 3/10
- (d) 2/5
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Explanations:
Part (a)
There is only one disc labeled "3" out of 10 total. So we end up with the probability 1/10.
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Part (b)
The list of numbers less than 4 are {1,2,3} which are 3 items out of 10 discs. We end up with 3/10.
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Part (c)
A square number, aka a perfect square, smaller than 10 is the list {1,4,9}
Since 1 = 1^2, 4 = 2^2 and 9 = 3^2
Like part (b), we end up with the same result of 3/10.
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Part (d)
The list of primes smaller than 10 is {2, 3, 5, 7}. Notice that 1 is not prime.
So we end up with 4/10 = 2/5.
The values of c and d which makes the given equations true are 7 and 5 respectively.
<h3>What is an exponent?</h3>
An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
<h3>How to determine the value of c and d?</h3>
From equation A, we have:
c = 7.
From equation B, we have:
![\sqrt[3]{576x^d} = 4x\sqrt[3]{9x^2} \\\\\sqrt[3]{576x^d} = \sqrt[3]{9x^2 \times (4x)^3}\\\\\sqrt[3]{576x^d} = \sqrt[3]{9x^2 \times 64x^3}\\\\\sqrt[3]{576x^d} = \sqrt[3]{9 \times 64x^{3+2}}\\\\\sqrt[3]{576x^d} = \sqrt[3]{576x^{5}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B576x%5Ed%7D%20%3D%204x%5Csqrt%5B3%5D%7B9x%5E2%7D%20%5C%5C%5C%5C%5Csqrt%5B3%5D%7B576x%5Ed%7D%20%3D%20%5Csqrt%5B3%5D%7B9x%5E2%20%5Ctimes%20%284x%29%5E3%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7B576x%5Ed%7D%20%3D%20%5Csqrt%5B3%5D%7B9x%5E2%20%5Ctimes%2064x%5E3%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7B576x%5Ed%7D%20%3D%20%5Csqrt%5B3%5D%7B9%20%5Ctimes%2064x%5E%7B3%2B2%7D%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7B576x%5Ed%7D%20%3D%20%5Csqrt%5B3%5D%7B576x%5E%7B5%7D%7D)
d = 5.
Read more on equation here: brainly.com/question/20352494
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